Green’s latest live movie experience will have its Boston premiere on Saturday
, with two performances at the Institute of Contemporary Art. The documentary chronicles the life and influence of Richard Buckminster Fuller, the architect and thinker most famous for his work developing the geodesic dome. As Green narrates onstage and cues images and video, longstanding indie rock trio Yo La Tengo performs its own original score.

Green, who codirected the 2002 Oscar-nominated documentary “The Weather Underground,” says in a phone interview that he stumbled into the genre of what he calls “live documentary.” With “Utopia in Four Movements,” which ran at the ICA in February 2011, he had tried to make a movie in the vein of Errol Morris’s “Fast, Cheap & Out of Control,” where disparate stories are linked by unstated themes. But viewers weren’t seeing the connections. Fuller decided some explanation might be necessary, and what was originally a presentation about the film became its essential form.

When the San Francisco Museum of Modern Art asked Green to make a live film about Fuller, he decided to make the experience even more specific to its environment. He adds tidbits about Fuller’s influence on each city that the movie visits.

“It takes . . . the challenge and interest in doing something live even further,” he says in a phone interview. “It goes back to old, old film, in the early 1900s. Some photographers would travel around to towns and shoot a bunch of portraits, and show them that night. It was a big deal because people would see themselves up on the screen.”

Adapting it for a Boston audience, he says, will be easy: Fuller was born in Milton, kicked out of Harvard twice (“officially for cutting my classes, but in fact for general irresponsibility,” Fuller once wrote), and buried in Mount Auburn Cemetery. But in other places it’s more of a challenge.

“It’s a little bit like a high wire act — can I do it everywhere?” Green says. “So far it’s worked.” Since premiering in San Francisco, the film has toured to Portland, Ore., Seattle, and Ithaca, N.Y.

The live score is a big part of the attraction. Yo La Tengo has experience with scoring film — the band’s credits include “Adventureland,” “Junebug,” and “Old Joy.” After seeing the band perform its soundtrack to the avant-garde films of Jean Painlevé, Green was inspired to tap them for the project.

“That was one of the greatest cinematic experiences I’ve ever had,” says Green. “I was enraptured.”

Because Yo La Tengo was also busy working on a new album (set to be released in January), Green visited the trio and gave them feedback in person as they rehearsed the score. Though it saved time, the band had to adjust to having another person in the practice space.

“It’s a lot tenser,” Yo La Tengo cofounder Ira Kaplan says with a laugh over the phone. “The three of us are used to working with just the other two. . . . Because we’ve been playing so long, we have our own language. To bring someone else into it — anybody, whether it’s Sam or another filmmaker — it changes the dynamic deeply.”

Because of the film’s format, Green felt a responsibility to ensure that the band felt good about the soundtrack. Normally, he said, the musicians are removed from the process once they finish recording.

“It was really important to me that they feel comfortable and like the musical parts, because they’ll be playing it in front of people,” Green says. “There’s no way I could say, ‘Listen man, it’s got to be this way.’ ”

For Kaplan, the collaborative process pushed creativity.

“I love the challenge,” he says. “When you change the working method, it’s always intriguing. It makes the hard parts worth it.”

The collaboration has continued beyond the rehearsal space and adds to the film’s spontaneity. Before a recent performance, Green says the band suggested shifting some of his narration to cue a break in a song with the film’s final image. After some maneuvering, Green decided the move would fit — or so it seemed.

“It’s funny because the last show we did, somehow it didn’t quite work,” Green says. “It’s fun to try and make things work in the moment. . . . Hopefully in Boston we’ll nail that end.”

“The Love Song of R. Buckminster Fuller,” with live accompaniment by Yo La Tengo, screens at the ICA, 100 Northern Ave., Boston,
Oct. 20 at 7 and 9 p.m. Tickets: $20-$25. For more information call 617-478-3103 or visit www.icaboston.org.

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